True confessions of a math major

I admit it. I don’t know, from memory, what 7 × 8 is. Every time I need to know the value of 7 × 8, I think to myself, Seven times seven is 49, plus 7 more is 56.

To tell you the truth, I also do something similar for 7 + 8. I don’t look at that and just know the sum is 15. I think, Seven plus seven is 14, plus one more is 15. Or, sometimes, Seven plus three is 10, plus 5 more is 15. I know a lot more addition facts from rote memory than I do multiplication facts, but I still often have to derive them. And I have a mathematics degree.

If your reaction to this confession is, So what?, I don’t blame you at all. Even though I’ve been at least partially aware of my fact derivation habits for as long as I can remember, I never talked about them until 6 or 7 years ago. They seemed utterly unremarkable and uninteresting. I thought everyone thought about numbers this way.

That turned out to be untrue. When I started working in curriculum development for early elementary school, I learned that one of the great debates in this realm is about student memorization of basic facts. Most researchers and curriculum developers seem to be in agreement that students need to have facility with basic facts. They are a building block for solving more complex problems. The debate rages around how to promote students’ learning of facts.

The primary instructional strategy for this for a long, long time, was to have students take timed facts tests. Answer these 100 addition and subtraction facts in 90 seconds! Young students were pushed to memorize the facts early so the curriculum could simply move on to other, more complex mathematics topics. However, it turns out that timed testing is associated with higher levels of math anxiety (Ashcraft & Moore, 2009). The timed tests, although intended to help kids build a strong mathematical foundation, actually have the effect of turning a lot of kids away from interest in mathematics. So, there’s been a push against timed testing.

Critics ask, Well, what are we to do instead? Just let kids count on their fingers for the rest of their lives? Nope. There are other ways to think about facts and fact learning. One strategy, of strong personal interest to me, is being explicit about teaching kids derivation strategies like the ones I use. I think of it as the difference between giving a kid a fish and teaching a kid to fish. You can force-feed kids the product 7 × 8, or you can teach kids how to figure it out quickly when memory fails.

In short, my personal story is this: The only time in my life I’ve ever hated math is when I had to take timed fact drills in elementary school. The fact that I have to derive 7 × 8 has never been a problem for me because I have strategies for figuring it out quickly and mentally. So I think, on a personal level, that we need to be teaching fact strategies.

I know my own personal story isn’t going to get much traction in the research realm, though. So imagine my excitement when I conducted a study with a colleague that used data from hundreds of thousands of kids to illustrate the promise of a strategy-based approach to fact learning. Read a brief guest blog post about the study here, on McGraw-Hill’s website. If you’ll be at NCTM on Tuesday, come and see my talk to hear about the study in more detail.